Question

Solve the following system of equations using the substitution method.

6x + 3y = 18

y = –2x + 5
Question 15 options:

A)

(3, –1)

B)

No solution

C)

Infinitely many solutions

D)

(15, 18)

Answer 1

B

Explanation:

First label the equations.

6x +3y= 18 -----(1)

y= -2x +5 -----(2)

subst. (2) into (1):

6x +3(-2x +5)= 18

6x +3(-2x) +3(5)= 18 (expand)

6x -6x +15= 18

15= 18 (simplify)

(reject)

There is no solution.

Further explanation:

If I rewrite the first equation into the form of y=mx+c, I would get

6x +3y=18

3y= 18 -6x (bring y term to one side)

y= 6- 2x (÷3 throughout)

y= -2x +6

Notice that the gradients of both lines are equal ( -2). This implies that they are parallel to each other and will never meet. Hence there are no solutions.